The Ratio of Proton Mass in Radon to Atomic Mass of Radon: Decimal Fraction Quiz
The ratio of the mass of the protons in radon to the atomic mass of radon
Question: The ratio of the mass of the protons in radon to the atomic mass of radon is 0.387387387. Write the decimal as a fraction.
Options:
A) 387/1000
B) 387/100
C) 387/10000
D) 3873/10000
Final answer:
The repeating decimal 0.387387387 is expressed as the fraction 387/999, which simplifies to 129/333. None of the options provided match this correct fraction.
Explanation:
The ratio of the mass of the protons in radon to the atomic mass of radon is given as 0.387387387. To write this decimal as a fraction, we notice the repeating pattern '387' and can express it as 387/999. This is because '387' repeats indefinitely making the decimal a repeating decimal, which corresponds to the fraction where the numerator is the repeating sequence and the denominator consists of the same number of 9's as there are digits in the repeating sequence.
By simplifying the fraction 387/999, we can divide the numerator and the denominator by 3, which results in 129/333. This is not one of the provided options, but it is the correct fraction for the repeating decimal 0.387387387. Hence, none of the options A, B, C, or D is correct.